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On singularities of Super Conformal Field Theories

Carefully studying the singularity structure of the moduli space of vacua of super conformal field theories, provides an incredibly powerful tool to extract information about such theories. In particular I will outline a concrete, yet technically challenging, strategy to go about carrying out a classification for SCFTs with extended supersymmetry in 4d.

I will explain in details how this classification has been worked out successfully for N=2 SCFTs in rank-1 and it is very promising in rank-2. And how with even higher Supersymmetry (N≥3) we can obtain a classification valid for all ranks making a few reasonable, yet key, assumptions.